Geometry prerequisite

Abstract

This chapter revisits some basic concepts from projective geometry, algebraic geometry and computer algebra. For projective geometry, we present, first intuitively then more formally, the concepts of homogeneous coordinates and projective spaces. Then we introduce metric properties using a projective language, paving the way for camera modeling. For algebraic geometry and computer algebra, we primarily target the introduction of the Gröbner basis and eigenvalue methods for solving polynomial systems of vision geometry problems. The purpose is to provide a minimum for readers to be able to follow the book. More refined and detailed treatment of the topics can be found in the excellent textbooks [196] for projective geometry and [27, 26] for algebraic geometry and computer algebra.